scholarly journals Pattern formation on the free surface of a ferrofluid: Spatial dynamics and homoclinic bifurcation

2017 ◽  
Vol 350 ◽  
pp. 1-12 ◽  
Author(s):  
M.D. Groves ◽  
D.J.B. Lloyd ◽  
A. Stylianou
Keyword(s):  
Free Surface ◽  
Pattern Formation ◽  
Spatial Dynamics ◽  
Homoclinic Bifurcation

scholarly journals Instabilities produced by hot-wire heating below a free surface with emphasis on relationships between temporal and spatial dynamics

1994 ◽  
Vol 4 (8) ◽  
pp. 1243-1260 ◽  
Author(s):  
E. Ringuet ◽  
S. Meunier-Guttin-Cluzel ◽  
C. Rozé ◽  
G. Gouesbet
Keyword(s):  
Free Surface ◽  
Spatial Dynamics ◽  
Hot Wire ◽  
Temporal And Spatial

NONLINEAR DYNAMICS NEAR THE CELL MEMBRANE OFCHARA CORALLINA

2008 ◽  
Vol 16 (02) ◽  
pp. 197-217 ◽  
Author(s):  
T. YU. PLYUSNINA ◽  
A. I. LAVROVA ◽  
C. B. PRICE ◽  
G. YU. RIZNICHENKO ◽  
A. B. RUBIN
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Pattern Formation ◽  
Cell Membrane ◽  
Transmembrane Potential ◽  
Nonlinear Partial Differential Equations ◽  
Spatial Dynamics ◽  
Chara Corallina ◽  
Potential Generation ◽  
Concentration Changes

The phenomenon of patterned distribution of pH near the cell membrane of the algae Chara corallina upon illumination is well-known. In this paper, we develop a mathematical model, based on the detailed kinetic analysis of proton fluxes across the cell membrane, to explain this phenomenon. The model yields two coupled nonlinear partial differential equations which describe the spatial dynamics of proton concentration changes and transmembrane potential generation. The experimental observation of pH pattern formation, its period and amplitude of oscillation, and also its hysteresis in response to changing illumination, are all reproduced by our model. A comparison of experimental results and predictions of our theory is made. Finally, a mechanism for pattern formation in Chara corallina is proposed.

scholarly journals Spatial correlations constrain cellular lifespan and pattern formation in corneal epithelium homeostasis

eLife ◽  
2021 ◽  
Vol 10 ◽  
Author(s):  
Lior Strinkovsky ◽  
Evgeny Havkin ◽  
Ruby Shalom-Feuerstein ◽  
Yonatan Savir
Keyword(s):  
Pattern Formation ◽  
Spatial Correlation ◽  
Corneal Epithelium ◽  
Spatial Dynamics ◽  
Cell Replication ◽  
Spatial Correlations ◽  
Replicative Lifespan ◽  
Tissue Integrity ◽  
Spatial Correlation Length

Homeostasis in adult tissues relies on the replication dynamics of stem cells, their progenitors and the spatial balance between them. This spatial and kinetic coordination is crucial to the successful maintenance of tissue size and its replenishment with new cells. However, our understanding of the role of cellular replicative lifespan and spatial correlation between cells in shaping tissue integrity is still lacking. We developed a mathematical model for the stochastic spatial dynamics that underlie the rejuvenation of corneal epithelium. Our model takes into account different spatial correlations between cell replication and cell removal. We derive the tradeoffs between replicative lifespan, spatial correlation length, and tissue rejuvenation dynamics. We determine the conditions that allow homeostasis and are consistent with biological timescales, pattern formation, and mutants phenotypes. Our results can be extended to any cellular system in which spatial homeostasis is maintained through cell replication.

Existence of spatiotemporal patterns in the reaction–diffusion predator–prey model incorporating prey refuge

2016 ◽  
Vol 09 (06) ◽  
pp. 1650085 ◽  
Author(s):  
Lakshmi Narayan Guin ◽  
Benukar Mondal ◽  
Santabrata Chakravarty
Keyword(s):  
Pattern Formation ◽  
Spatial Dynamics ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Model System ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

The pattern formation in reaction–diffusion system has long been the subject of interest to the researchers in the domain of mathematical ecology because of its universal existence and importance. The present investigation deals with a spatial dynamics of the Beddington–DeAngelis predator–prey model in the presence of a constant proportion of prey refuge. The model system representing boundary value problem under study is subjected to homogeneous Neumann boundary conditions. The asymptotic stability including the local and the global stability and the bifurcation as well of the unique positive homogeneous steady state of the corresponding temporal model has been analyzed. The Turing instability region in two-parameter space and the condition of diffusion-driven instability of the spatiotemporal model are investigated. Based on the appropriate numerical simulations, the present model dynamics in Turing space appears to get influenced by prey refuge while it exhibits diffusion-controlled pattern formation growth to spots, stripe-spot mixtures, labyrinthine, stripe-hole mixtures and holes replication. The results obtained appear to enrich the findings of the model system under consideration.

scholarly journals Pattern formation in bubbles emerging periodically from a liquid free surface

2010 ◽  
Vol 33 (1) ◽  
pp. 11-18 ◽  
Author(s):  
H. N. Yoshikawa ◽  
C. Mathis ◽  
P. Maıssa ◽  
G. Rousseaux ◽  
S. Douady
Keyword(s):  
Free Surface ◽  
Pattern Formation ◽  
Liquid Free Surface

scholarly journals Pattern Dynamics in a Spatial Predator-Prey System with Allee Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Gui-Quan Sun ◽  
Li Li ◽  
Zhen Jin ◽  
Zi-Ke Zhang ◽  
Tao Zhou
Keyword(s):  
Pattern Formation ◽  
Mortality Rate ◽  
Allee Effect ◽  
Spatial Dynamics ◽  
Spiral Wave ◽  
Amplitude Equations ◽  
Predator Prey ◽  
Pattern Dynamics ◽  
Prey System ◽  
The Stability

We investigate the spatial dynamics of a predator-prey system with Allee effect. By using bifurcation analysis, the exact Turing domain is found in the parameters space. Furthermore, we obtain the amplitude equations and determine the stability of different patterns. In Turing space, it is found that predator-prey systems with Allee effect have rich dynamics. Our results indicate that predator mortality plays an important role in the pattern formation of populations. More specifically, as predator mortality rate increases, coexistence of spotted and stripe patterns, stripe patterns, spotted patterns, and spiral wave emerge successively. The results enrich the finding in the spatial predator-prey systems well.

Wave pattern formation in a fluid annulus with a radially vibrating inner cylinder

1996 ◽  
Vol 328 ◽  
pp. 229-252 ◽  
Author(s):  
T. S. Krasnopolskaya ◽  
G. J. F. Van Heijst
Keyword(s):  
Free Surface ◽  
Pattern Formation ◽  
Parametric Resonance ◽  
Standing Waves ◽  
Wave Pattern ◽  
Free Surface Waves ◽  
Symmetric Wave ◽  
Wave Patterns ◽  
The Waves ◽  
Theoretical Results

The phenomenon of pattern formation of free-surface waves of a fluid confined in an annulus the inner wall of which vibrates radially, is investigated both theoretically and experimentally. Although the waves are excited by harmonic axisymmetric deformations of the inner shell, depending on the vibration frequency both axisymmetric and non-symmetric wave patterns may arise.Experimental observations have revealed that waves are excited in two different resonance regimes. The first type corresponds to forced resonance, in which axisymmetric patterns are realized with eigenfrequencies equal to the frequency of excitation. The second kind is parametric resonance, in which case the waves are ‘transverse’, with their crests and troughs aligned perpendicular to the vibrating wall. These so-called cross-waves have frequencies equal to half of that of the wavemaker.Both kinds of resonance were investigated theoretically using Lamé's method of superposition. It was shown experimentally that the pure forced resonant standing waves are not realized when the amplitude of excitation is beyond the threshold of parametric resonance for non-symmetric waves. The experimental observations agree very well with the theoretical results.

On the role of tin underlays for the prevention of thermal grooving in thin gold films

1986 ◽  
Vol 44 ◽  
pp. 732-733
Author(s):  
Jin Young Kim ◽  
R. E. Hummel ◽  
R. T. DeHoff
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Grain Boundary ◽  
Beneficial Effect ◽  
Failure Mechanism ◽  
Failure Mechanisms ◽  
Distinct Advantage ◽  
Gold Films ◽  
Gold Thin Film

Gold thin film metallizations in microelectronic circuits have a distinct advantage over those consisting of aluminum because they are less susceptible to electromigration. When electromigration is no longer the principal failure mechanism, other failure mechanisms caused by d.c. stressing might become important. In gold thin-film metallizations, grain boundary grooving is the principal failure mechanism.Previous studies have shown that grain boundary grooving in gold films can be prevented by an indium underlay between the substrate and gold. The beneficial effect of the In/Au composite film is mainly due to roughening of the surface of the gold films, redistribution of indium on the gold films and formation of In2O3 on the free surface and along the grain boundaries of the gold films during air annealing.

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